Comprehensive immigration reform legislation cleared a critical hurdle Monday, with a bipartisan majority green-lighting a compromise measure to dramatically beef up the bill's border security provisions and help pave the way for final passage of the overhaul.

NBC's Domenico Montanaro discusses the latest on the immigration reform debate on Capitol Hill, and the latest Supreme Court decision handed down Monday. Plus, where in the world is Edward Snowden?

The procedural vote to cut off debate on the so-called “border surge” amendment -- introduced by Republicans Bob Corker of Tennessee and John Hoeven of North Dakota -- was passed 67-27, with 15 Republicans voting with all Democrats in favor of the measure. (Several senators did not vote due to reported travel delays.)

The passage is welcome news to bill backers who are aiming for a strong vote for the overall legislation's final passage, which remains on track for this week before the Senate recesses for its Fourth of July break.

The compromise proposal would double the number of border patrol agents along the nation’s southern border and would mandate the completion of 700 miles of fencing. Critics say it is far too costly and still lacks robust enough “triggers” to ensure that the border is adequately secured.

The Republican duo and the bill’s original bipartisan drafters hammered out the legislative addition last week in order to woo additional conservative votes to support the overall “Gang of Eight” bill.

Their efforts yielded a modest but important new influx of GOP support. Aye votes on the Corker-Hoeven procedural test included Sens. Roger Wicker of Mississippi, Orrin Hatch of Utah, Dean Heller of Nevada, Mark Kirk of Illinois, and Jeff Chiesa of New Jersey -- although not all will likely support the overall bill later this week.

Senate Minority Leader Mitch McConnell joined opponents of the bill Monday in opposing the border surge measure, saying he is “not convinced” the proposed fixes would ensure a truly secure border.

“Despite the hard work and best efforts of our colleagues, I remain concerned that when it comes to the threshold question of border security, today's assurances may well become tomorrow's disappointments,” he said in a statement.

Supporters were buoyed late Monday when a preliminary analysis from the Congressional Budget Office confirmed that the new language would substantially reduce the flow of undocumented workers into the country. (The report also found that the changes would shave billions off the original projected savings for federal coffers over the next 10 years, a cost that sponsors say will still be offset by new revenues.)

Republican authors of the border security measure also got a boost over the weekend from Gov. Jan Brewer of Arizona, an outspoken GOP critic of the Obama administration on immigration policy, who called the new proposal a "victory." She added via Twitter Monday that she has not endorsed the underlying "Gang of Eight" bill but that she's optimistic that Republicans in the House will help improve the legislation to make it "workable."

"Do you really want to vote against an amendment that the governor of Arizona - who has dealt with this issue more closely than any of us in this body - has declared as a total victory for their state? You want to vote against this?" Corker asked during impassioned remarks on the Senate floor.

Backers of the overall legislation – which would also offer undocumented immigrants a path to legal status and eventual citizenship – hope that a robust bipartisan vote on the Senate floor will push Republican House Speaker John Boehner to take up the immigration issue in the lower chamber.

“This bill will pass with votes from both Democrats and Republicans, and, when it does, the Speaker should bring it up for a vote in the House of Representatives as well,” Democratic Senate Majority Leader Harry Reid said Monday in remarks aimed at the Republican leader. “Rather than twisting the arms of Tea Party extremists, just work with moderates from both parties to pass bipartisan legislation.”

But Reid's suggestion is a highly unlikely path; Boehner has repeatedly stated that the House will work on its own legislation and that he will not allow a bill to the floor that does not have a majority of support from his own party.

While the Hoeven-Corker measure has won over a substantial number of Republicans, a bloc of GOP lawmakers who object to the underlying bill are far from enthusiastic about the new border security proposal.

With media appearances, barrages of tweets and fiery Senate floor speeches, opponents of the legislation have painted the amendment as a “fig leaf” that ensures only the expenditure of billions of federal dollars but not the desired results.

Sen. Ted Cruz of Texas, a leading opponent of the bill, has launched an online petition against the amendment, which he says is only a “false promise” of border security that will allow a new wave of illegal immigration into the country and will be tantamount to “amnesty.”

Cruz and others also contend that Reid rushed the amendment to the Senate floor without giving senators sufficient time to review the new legislative language hammered out in negotiations last week.

A total of 14 Republican senators wrote to Reid Monday to air complaints with the legislative process, accusing the Democratic leader of stonewalling other Republican attempts to improve the bill.

Reid spokesman Adam Jentleson said that complaint was far from genuine, pointing the finger back at GOP senators for stopping amendment votes over the past two weeks of Senate debate.

“Senator Reid takes the concerns of senators on both sides of the aisle very seriously, but the senators who signed this letter are the same senators who have been preventing amendment votes from occurring throughout this process,” he said. “This letter is nothing more than a transparent attempt to suppress the strong bipartisan support for immigration reform.”